# Orbital velocity and gravity calculator

> Orbital velocity and period, escape velocity, surface gravity, your weight on the Moon or Mars, and the gravitational force between two masses.

انٹرایکٹو صورت: https://www.calcopenly.com/ur/science/gravity-orbit-calculator
موضوع: سائنس کے کیلکولیٹر

Newton's law of gravitation, F = Gm₁m₂/r², gives the pull between two masses. For a body of mass M the same law sets the speed of a circular orbit, v = √(GM/r), its period from Kepler's third law, T = 2π√(r³/GM), the escape velocity √(2GM/r) and the surface gravity GM/R². Pick the Earth, Moon, Mars, Jupiter or the Sun, or enter any mass and radius.

The default, an orbit 400 km above Earth like the International Space Station's, gives 7.67 km/s (about 17,200 mph) and 92.4 minutes per lap. Entering one sidereal day, 23.934 hours, as the period returns the geostationary radius of 42,164 km.

Radii are volumetric means from NASA's fact sheets and rotation is ignored, so Earth's surface gravity comes out at 9.82 m/s², between the 9.78 m/s² measured at the equator and 9.83 m/s² at the poles. Orbits are circular and drag-free.

## اندراجات

- **Calculate** (اختیارات: Circular orbit, Escape velocity, Surface gravity, Force between masses)
- **جسم** (اختیارات: Earth, Moon, Mars, Jupiter, Sun, Custom)
- **Body mass**
- **Body radius**
- **Given** (اختیارات: Altitude → speed and period, Period → altitude)
- **Altitude above the surface**
- **Orbital period**: 23.9344696 h is one sidereal day (geostationary orbit)
- **Your mass (for weight there)**
- **نتائج کی اکائی** (اختیارات: km, m/s, N, mi, mph, lbf)
- **Mass 1**
- **Mass 2**
- **Centre-to-centre distance**

## نتائج

- Orbital speed (m/s) — بنیادی نتیجہ
- Orbital period
- Orbital period (h)
- Altitude above the surface (km)
- Orbit radius from the centre (km)
- Escape velocity from that altitude (m/s)
- Surface gravity (m/s²)
- Surface gravity (g)
- Your weight there (N)
- Gravitational force (N)
- Gravitational parameter GM (m³/s²)

## فارمولا

$$
F = \frac{Gm_1m_2}{r^2},\quad v = \sqrt{\frac{GM}{r}},\quad T = 2\pi\sqrt{\frac{r^3}{GM}},\quad v_{\text{esc}} = \sqrt{\frac{2GM}{r}},\quad g = \frac{GM}{R^2}
$$

## حل شدہ مثالیں

### ISS-like orbit at 400 km

- Calculate: Circular orbit
- جسم: Earth
- Given: Altitude → speed and period
- Altitude above the surface: 400 km
- نتائج کی اکائی: km, m/s, N
- **Orbital speed: 7,672.62 m/s**
- **Orbital period: 1.54023 h**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h⁩

### Geostationary altitude from one sidereal day

- Calculate: Circular orbit
- جسم: Earth
- Given: Period → altitude
- Orbital period: 23.9344696 h
- نتائج کی اکائی: km, m/s, N
- **Altitude above the surface: 35,793.2 km**
- **Orbital speed: 3,074.67 m/s**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: r = (GM T²/4π²)^⅓ = 42164.2 km (the published GEO radius); minus the 6371 km mean radius (35,786 km is quoted above the 6378 km equatorial radius)⁩

### Orbit skimming the surface (altitude 0)

- Calculate: Circular orbit
- جسم: Earth
- Given: Altitude → speed and period
- Altitude above the surface: 0 km
- نتائج کی اکائی: km, m/s, N
- **Orbital speed: 7,909.81 m/s**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: √(GM/R) with R = 6371.0 km = 7909.813⁩

### Escape velocity from Earth's surface

- Calculate: Escape velocity
- جسم: Earth
- Altitude above the surface: 0 km
- نتائج کی اکائی: km, m/s, N
- **Escape velocity from that altitude: 11,186.2 m/s**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: √(2GM/R) = 11186.165 m/s (NASA fact sheet lists 11.186 km/s)⁩

### Surface gravity on the Moon

- Calculate: Surface gravity
- جسم: Moon
- Your mass (for weight there): 70 kg
- نتائج کی اکائی: km, m/s, N
- **Surface gravity: 1.62427 m/s²**
- **Your weight there: 113.699 N**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: G × 7.346e22 / 1737400² = 1.624265 m/s² (NASA lists 1.62); × 70 kg = 113.699 N⁩

### Two 1 kg masses 1 m apart

- Calculate: Force between masses
- Mass 1: 1 kg
- Mass 2: 1 kg
- Centre-to-centre distance: 1 m
- **Gravitational force: 6.6743 × 10⁻¹¹ N**
- جانچ کا ماخذ: ⁨Newton's law with G (CODATA 2022): F = G·1·1/1² = 6.6743 × 10⁻¹¹ N⁩

## سوالات

### How fast does the International Space Station orbit Earth?

About 7.67 km/s at 400 km altitude, which is 27,600 km/h or roughly 17,200 mph, and one lap takes 92.4 minutes. The speed depends only on Earth's GM and the orbit radius (6,771 km here), not on the station's mass. Raising the orbit to 410 km slows it by 5.7 m/s and lengthens the lap by 12 seconds.

### What is the escape velocity of Earth?

11.186 km/s from the surface, about 40,270 km/h, the figure on NASA's Earth fact sheet. It is the speed at which an unpowered object never falls back, ignoring air drag, and it is the same for a pebble and a rocket. The Moon's is 2.38 km/s, Mars's 5.03 km/s and Jupiter's about 60 km/s. From 400 km up it drops to 10.85 km/s.

### Why is escape velocity √2 times orbital velocity?

Escaping takes twice the kinetic energy of a circular orbit at the same height. In a circular orbit the kinetic energy is GMm/2r; reaching infinity needs GMm/r, the full depth of the potential well. Doubling kinetic energy multiplies speed by √2 ≈ 1.414, so the 7.67 km/s orbital speed at 400 km above Earth becomes an escape speed of 10.85 km/s.

### How high is a geostationary orbit?

35,786 km above the equator, a radius of 42,164 km from Earth's centre. At that radius Kepler's third law gives a period of one sidereal day, 23 h 56 min 4 s, so the satellite keeps pace with Earth's rotation. Entering that period here gives the same radius and an altitude of 35,793 km, because the calculator subtracts the 6,371 km mean radius rather than the 6,378 km equatorial radius.

### How much would I weigh on the Moon or Mars?

About 16.6% of your Earth weight on the Moon and 38% on Mars. Surface gravity GM/R² is 1.62 m/s² on the Moon and 3.73 m/s² on Mars with NASA's mean radii, against the 9.80665 m/s² standard gravity defined for Earth. A 70 kg person weighs 113.7 N on the Moon, which a scale calibrated on Earth would show as 11.6 kg.

### “⁨Orbital velocity and gravity calculator⁩” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 8۔ مثلاً، “⁨ISS-like orbit at 400 km⁩” کو ⁨Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h⁩ سے جانچا جاتا ہے۔

### اس طریقے کا ماخذ کیا ہے؟

OpenStax University Physics Volume 1, ch. 13 Gravitation (§13.5 Satellite orbits, §13.3 Escape velocity); CODATA 2022 — Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²; NASA Planetary Fact Sheets (mass, volumetric mean radius).

## ماخذ

- [OpenStax University Physics Volume 1, ch. 13 Gravitation (§13.5 Satellite orbits, §13.3 Escape velocity)](https://openstax.org/books/university-physics-volume-1/pages/13-4-satellite-orbits-and-energy)
- [CODATA 2022 — Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²](https://physics.nist.gov/cgi-bin/cuu/Value?bg)
- [NASA Planetary Fact Sheets (mass, volumetric mean radius)](https://nssdc.gsfc.nasa.gov/planetary/factsheet/)